Question

A bag contains 15 marbles. The probability of randomly selecting a green marble is 1/5. The probability of randomly selecting a green marble, replacing it, and then randomly selecting a blue marble is 2/25. How many blue marbles are in the bag?

2

3

5

6

Answer 1

6 blue marbles

Explanation:

Given;

Total number of marbles N = 15

probability of randomly selecting a green marble

P(G) = 1/5

The probability of randomly selecting a green marble, replacing it, and then randomly selecting a blue marble P(G∩B) = 2/25

P(G∩B) = P(G) × P(B)

P(B) = P(G∩B) ÷ P(G)

The probability of selecting a blue marble

P(B) = 2/25 ÷ 1/5 = 2/5

The number of blue marbles N(B) = P(B) × N

N(B) = 2/5 × 15 = 6

There are 6 blue marbles